Open AccessEfficient linearized local energy-preserving method for the Kadomtsev-Petviashvili equation
Author(s) -
Jiaxin Cai,
Chen Juan,
Min Chen
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021139
Subject(s) - symplectic geometry , discretization , mathematics , scheme (mathematics) , backward euler method , hamiltonian (control theory) , euler's formula , soliton , mathematical analysis , nonlinear system , mathematical optimization , physics , quantum mechanics
A linearized implicit local energy-preserving (LEP) scheme is proposed for the KPI equation by discretizing its multi-symplectic Hamiltonian form with the Kahan's method in time and symplectic Euler-box rule in space. It can be implemented easily, and also it is less storage-consuming and more efficient than the fully implicit methods. Several numerical experiments, including simulations of evolution of the line-soliton and lump-type soliton and interaction of the two lumps, are carried out to show the good performance of the scheme.